ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of TiPN3 (Materials Project id mp-989613)

       388      113       66        0        0        0  
       113      196       97        0        0        0  
        66       97      448        0        0        0  
         0        0        0       53        0        0  
         0        0        0        0       91        0  
         0        0        0        0        0       34  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 176 GPaEV = 221.86 GPaGV = 86 GPaνV = 0.2899
ReussKR = 159.67 GPaER = 166.41 GPaGR = 62.737 GPaνR = 0.3263
HillKH = 167.84 GPaEH = 194.39 GPaGH = 74.368 GPaνH = 0.30696

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
34 GPa 53 GPa 91 GPa 130.93 GPa 351.48 GPa 549.59 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 109.53 GPa 399.68 GPa 1.2307 TPa–1 3.7589 TPa–1 34 GPa 173.67 GPa0.0312110.67946Value
Anisotropy 3.649 3.0543 5.108 21.7700Anisotropy
Axis -0.6231
0.7821
-0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
-0.0002
0.0000
0.7071
-0.0000
-0.7071
0.0000
0.0000
1.0000
-0.8584
0.5130
-0.0000
Axis
0.0002
1.0000
0.0001
-0.7071
0.0002
-0.7071
-1.0000
0.0000
0.0000
-0.5130
-0.8584
-0.0000
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane